A large number of signal processing applications, ranging from surveillance cameras to automobiles to airplanes to UAVs, need to perform filtering operations on large volumes of signals that are acquired by numerous sensors in real time. For example, prior art object recognition algorithms employ a deep learning network whose fundamental computation is a convolution operation.
In the prior art, coupled oscillators have been used to compute a degree-of-match (DoM) between two vectors, as described in References [2], [7], and [8], below, which are incorporated herein by reference. A DoM is computed from the difference between the two vectors, and is based on the dynamics of spontaneous synchronization among the coupled oscillators. The concept is that if the vectors have similar values such that the match is high and the differences are small, then the oscillators synchronize in frequency and phase relatively quicker.
FIG. 1 shows a cluster of oscillators 10 that are weakly coupled to each other via an averager 12 to perform template matching. Individual oscillators 10 are either phase- or frequency-perturbed based on corresponding elements in the difference vector 18 between a five element input vector 14 and a five element vector template 16. The degree-of-match is read out by integrating the oscillation at the averager 12. A person skilled in the art will appreciate that an M dimensional input vector would require a cluster of M oscillators.
Depending on the oscillator behavior, for example as described in References [7] and [8] for a CMOS relaxation oscillator, and coupling architecture, which may be a ring as described in Reference [2], the output DoM measure has been shown to roughly correlate with some Lp norm of the distance between the vectors.
A person skilled in the art understands the formula for an Lp norm, and knows that the formula for an L2 norm of a vector x is
                  x              =                                        ∑                          k              =              1                        n                    ⁢                                                                  x                k                                                    2                              .        ,while the formula for an L1 norm is
                  x              1    =                    ∑                  r          =          1                n            ⁢                                x          r                              ..  
It has been challenging to characterize the DoM measure with a closed-form analytic function of an Lp norm that is differentiable everywhere. Being able to perform such a characterization of DoM is critical because the prior art pattern recognition and machine learning algorithms, which may for example use convolutional nets, or a hierarchy of auto-encoders, are trained using variants of gradient descent, which may for example be delta rule and back-propagation. Delta rule and back-propagation work only for differentiable activation functions for each of the vast number of units in the network. For this reason, existing attempts at exploiting the concept of oscillator clusters to build complex visual object recognition systems have achieved only limited success, as described in References [3] and [4], below, which are incorporated herein by reference. However, methods that use oscillator clusters but which do not depend on gradient descent training have been more successful, as described in References [7] and [8].